^{1,a)}, Toshiyuki Kohno

^{2}, Tatsuaki Kanai

^{3}, Yuki Kase

^{4}, Yoshitaka Matsumoto

^{5}, Yoshiya Furusawa

^{5}, Yukio Fujita

^{6}, Hidetoshi Saitoh

^{6}and Jun Itami

^{7}

### Abstract

**Purpose:**

Microdosimetry has been developed for the evaluation of radiation quality, and single-event dose-mean lineal energy is well-used to represent the radiation quality. In this study, the changes of the relative biological effectiveness (RBE) values under the therapeutic conditions using a 6 MV linac were investigated with a microdosimetric method.

**Methods:**

The values under the various irradiation conditions for x-rays from a 6 MV linac were measured with a tissue-equivalent proportional counter (TEPC) at an extremely low dose rate of a few tens of μGy/min by decreasing the gun grid voltage of the linac. According to the microdosimetric kinetic model (MK model), the RBE_{MK} values for cell killing of the human salivary gland (HSG) tumor cells can be derived if the values are obtained from TEPC measurements. The Monte Carlo code GEANT4 was also used to calculate the photon energy distributions and to investigate the changes of the values under the various conditions.

**Results:**

The changes of the values were less than approximately 10% when the field size and the depth in a phantom varied. However, in the measurements perpendicular to a central beam axis, large changes were observed between the values inside the field and those outside the field. The maximum increase of approximately 50% in the value outside the field was obtained compared with those inside the field. The GEANT4 calculations showed that there existed a large relative number of low energy photons outside of the field as compared with inside of the field. The percentages of the photon fluences below 200 keV outside the field were approximately 40% against approximately 8% inside the field. By using the MK model, the field size and the depth dependence of the RBE_{MK} values were less than approximately 2% inside the field. However, the RBE_{MK} values outside the field were 6.6% higher than those inside the field.

**Conclusions:**

The increase of the RBE_{MK} values by 6.6% outside the field was observed. This increase is caused by the change of the photon energy distributions, especially the increase of the relative number of low energy photons outside the field.

The authors would like to thank Dr. Y. Noda, Dr. K. Nishizawa, Dr. S. Yonai, and Dr. W. Yamashita for technical supports in the TEPC measurements.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. Electronics and experimental technique

II.B. Measurements of values for 6 MV x-rays with TEPC

II.C. Microdosimetric kinetic model

II.D. Monte Carlo simulation with GEANT4

III. RESULTS AND DISCUSSION

III.A. Verification of radiation quality at extremely low dose rate

III.B. Changes of photon energy distributions calculated with GEANT4

III.C. Properties of RBE for 6 MV x-rays

III.C.1. TEPC measurements

III.C.2. Field size dependence of RBE

III.C.3. Depth dependence of RBE

III.C.4. RBE at different positions perpendicular to central beam axis

III.D. Relation between RBE and low energy photons

IV. CONCLUSIONS

## Figures

The geometries of three kinds of the TEPC measurements: (a) the change of the field size and the change of the position perpendicular to the central beam axis (depth = 10 cm, and a source to surface distance = 90 cm) and (b) the change of the depth (a source to surface distance = 100 cm).

The geometries of three kinds of the TEPC measurements: (a) the change of the field size and the change of the position perpendicular to the central beam axis (depth = 10 cm, and a source to surface distance = 90 cm) and (b) the change of the depth (a source to surface distance = 100 cm).

The symbols represent the experimental RBE for cell killing of the HSG tumor cells for 200 kV x-rays (open circle), ^{60}Co γ-rays (open triangle), and 6 MV x-rays (open square), and the solid line represents the calculated RBE_{MK} using Eq. (6), which were reported in the previous paper (Ref. 4). 200 kV x-ray was defined as the reference radiation.

The symbols represent the experimental RBE for cell killing of the HSG tumor cells for 200 kV x-rays (open circle), ^{60}Co γ-rays (open triangle), and 6 MV x-rays (open square), and the solid line represents the calculated RBE_{MK} using Eq. (6), which were reported in the previous paper (Ref. 4). 200 kV x-ray was defined as the reference radiation.

(a) Comparison between the measured and the calculated depth-dose curve for a 10 × 10 cm^{2} field with 6 MV x-rays. The depth-dose curve was measured with an ionization chamber (CC13, Scanditronix–wellhofer). All the data were normalized to be unity at a depth of 10 cm. (b) Comparison between the measured and the calculated dose profile at a depth of 10 cm for a 40 × 40 cm^{2} field with 6 MV x-rays. A diode detector (PFD, Scanditronix–wellhofer) was used for the measurements.

(a) Comparison between the measured and the calculated depth-dose curve for a 10 × 10 cm^{2} field with 6 MV x-rays. The depth-dose curve was measured with an ionization chamber (CC13, Scanditronix–wellhofer). All the data were normalized to be unity at a depth of 10 cm. (b) Comparison between the measured and the calculated dose profile at a depth of 10 cm for a 40 × 40 cm^{2} field with 6 MV x-rays. A diode detector (PFD, Scanditronix–wellhofer) was used for the measurements.

Comparison between the relative depth dose at the clinical dose rate (RDD1) and that at the extremely low dose rate (RDD2).

Comparison between the relative depth dose at the clinical dose rate (RDD1) and that at the extremely low dose rate (RDD2).

The changes of the photon energy distributions (a) for the different field sizes, (b) for the different depths, and (c) for the various distances from the field edge (referred to as *X* _{edge}) for a 10 × 10 cm^{2} field, calculated with GEANT4. The three geometries are the same as those in the TEPC measurements. The total amount of fluence in each distribution is normalized to be unity. The size of energy bins is 0.1 MeV. The error bars represent the statistical uncertainty (1 SD).

The changes of the photon energy distributions (a) for the different field sizes, (b) for the different depths, and (c) for the various distances from the field edge (referred to as *X* _{edge}) for a 10 × 10 cm^{2} field, calculated with GEANT4. The three geometries are the same as those in the TEPC measurements. The total amount of fluence in each distribution is normalized to be unity. The size of energy bins is 0.1 MeV. The error bars represent the statistical uncertainty (1 SD).

Field size dependence of the measured values (left vertical axis) and the calculated RBE_{MK} for cell killing of the HSG tumor cells at the 10% survival level (right vertical axis). The error bars represent 1 SD of . An overall uncertainty of approximately 6% for the RBE_{MK} values, which is including both the error of the value and the error for the reproduction of the experimental RBE, is not shown in the figure.

Field size dependence of the measured values (left vertical axis) and the calculated RBE_{MK} for cell killing of the HSG tumor cells at the 10% survival level (right vertical axis). The error bars represent 1 SD of . An overall uncertainty of approximately 6% for the RBE_{MK} values, which is including both the error of the value and the error for the reproduction of the experimental RBE, is not shown in the figure.

Depth dependence of the measured values (left vertical axis) and the calculated RBE_{MK} for cell killing of the HSG tumor cells at the 10% survival level (right vertical axis). The error bars represent 1SD of . An overall uncertainty of approximately 6% for the RBE_{MK} values, which is including both the error of the value and the error for the reproduction of the experimental RBE, is not shown in the figure.

Depth dependence of the measured values (left vertical axis) and the calculated RBE_{MK} for cell killing of the HSG tumor cells at the 10% survival level (right vertical axis). The error bars represent 1SD of . An overall uncertainty of approximately 6% for the RBE_{MK} values, which is including both the error of the value and the error for the reproduction of the experimental RBE, is not shown in the figure.

The measured values (left vertical axis) and the calculated RBE_{MK} for cell killing of the HSG tumor cells at the 10% survival level (right vertical axis) perpendicular to the central beam axis for the different field sizes. The error bars (1SD) of only for a 1 × 1 cm^{2} field are typically shown in the figure, because those for the other field sizes are almost the same. An overall uncertainty of approximately 6% for the RBE_{MK} values, which is including both the error of the value and the error for the reproduction of the experimental RBE, is not shown in the figure.

The measured values (left vertical axis) and the calculated RBE_{MK} for cell killing of the HSG tumor cells at the 10% survival level (right vertical axis) perpendicular to the central beam axis for the different field sizes. The error bars (1SD) of only for a 1 × 1 cm^{2} field are typically shown in the figure, because those for the other field sizes are almost the same. An overall uncertainty of approximately 6% for the RBE_{MK} values, which is including both the error of the value and the error for the reproduction of the experimental RBE, is not shown in the figure.

Microdosimetric distributions *y-yd*(*y*) at the different positions perpendicular to the central beam axis for a 15 × 15 cm^{2} field. The open and the closed symbols represent the distributions inside and outside the field, respectively.

Microdosimetric distributions *y-yd*(*y*) at the different positions perpendicular to the central beam axis for a 15 × 15 cm^{2} field. The open and the closed symbols represent the distributions inside and outside the field, respectively.

The percentage of the photon fluence below 200 keV calculated with GEANT4 for the various field sizes. The total amount of fluence in each distribution is normalized to be unity. The error bars represent the statistical uncertainty (1 SD).

The percentage of the photon fluence below 200 keV calculated with GEANT4 for the various field sizes. The total amount of fluence in each distribution is normalized to be unity. The error bars represent the statistical uncertainty (1 SD).

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